Recently, a search for collisional deexcitation of the metastable nuclear isomer \(^{180m}\mbox{Ta}\)  induced by DM has led to novel constraints on IDM [1]}, [2]}. \(^{180m}\mbox{Ta}\)  is fairly unique: it is stable on time scales much larger than the age of the Universe, and its natural abundance is well established. As the isomers of other nuclei are short-lived, this method is not generally applicable. However, the excitation of ground state nuclei to excited states remains possible in the scattering \(\chi _1+N\rightarrow \chi _2+N^*\)  if the excitation energy is low enough [3]}, [4]}, [5]}. We focus on a few isotopes, with possible nuclear transitions that we will explore listed in Table REF  below. Once scattered into an excited state, the gamma quanta emitted during subsequent decay to the ground state can be measured. By measuring the activity of these transition lines, we may obtain a conservative upper bound on the total inelastic scattering rate from DM interactions, and thus on the DM-nucleon scattering cross section. In comparison with traditional direct detection experiments, this method appears rather insensitive. Indeed, nuclear excitation is more kinematically suppressed, and the scattering does not enjoy the usual \(A^2\)  enhancement factor because the DM is interacting with a single nucleon rather than scattering coherently with the full nucleus. However, we
identify two advantages: 1) The high mass of transition nuclei better matches heavier DM candidates, and 2) the energy of the outgoing gamma is independent of the recoil energy, since it is fixed by the structure of the target nucleus. This means that, for a given transition, there is no danger of the signal being lost outside of the analysis region of interest. Previously, we have performed such an analysis in the context of a search for rare decays of Hf [6]} and set stronger bounds on IDM mass splittings than previously-reported results from direct detection experiments. In this paper, we extend our approach, using previously-published data collected within low-background measurements with Hf and Os metal samples, along with the limits derived from bolometeric measurements using CaWO\(_4\)  and PbWO\(_4\)  scintillating crystals. Although the NE bounds that we find are not as strong as the NR bounds that we derive from bolometer measurements, we will identify a path to leading constraints on WIMPy inelastic dark matter using the nuclear properties of target materials.
